The WW2 service records are
in the process of being transferred to TNA. They are not all there yet!
When you apply for a British Army record (using the link in reply #3 above), the MoD will check if they hold it. If they do, they’ll send it to you. If they don't, you’ll be told to apply to TNA.
Records already at TNA are subject to Freedom of Information regulations, which greatly slows the application/delivery process. There is currently a wait of
up to about 18 months for army records, and they normally arrive in redacted form. TNA are working hard to speed up the process, but they are very understaffed.
Royal Navy and RAF records are generally quicker. Some RAF records were digitised by the MoD before the transfer began, and they may be sent out by the MoD within a week or two.
Most of the WW2 service records will eventually be digitised by Ancestry, who have already started the work.
For more detailed information on the background to the transfer and delivery of these records, please see ...
https://www.nationalarchives.gov.uk/about/our-role/plans-policies-performance-and-projects/our-projects/ministry-of-defence-service-records/